More detailed understandings of the spun-on planarization properties of thin films are becoming increasingly important in the field of integrated circuit processing. See articles in this field, for example, by D. W. Widmann and H. Binder, entitled "Linewidth Variations in Photoresist Patterns on Profiled Surfaces," IEEE Trans. Electron Devices, Vol. ED-22, No. 7, pp. 467-471 (July 1975 and M. M. O'Toole, E. D. Liu and M. S. Chang, entitled "Linewidth Control in Projection Lithography Using a Multilayer Resist Process, " IEEE Trans. Electron Devices, Vol. ED-28, No. 11, pp. 1405-1410 (November 1981). The property of planarization is the ability of a material applied to a surface by a spinning action of the substrate, receiving the material from a nozzle, moving radially thereover to cover the topography of the surface and reduce step heights. It has recently been discovered that the patterned dimensions of a film of resist that is deposited on uneven topographical features are strongly influencesd by the change in the thickness of the resist. Moreover, in the etching of the photoresist material to develop a pattern by a process which has been known as the dual-etch-back technique, the conformality of the passivation and isolation layers that are to be etched depend strongly on the spun-on, thin film planarization properties. See the article in this field by A. C. Adams and C. D. Capio, entitled "Planarization of Phosphorus-Doped Silicon Dioxide," J. Electrochem. Soc., Vol. 128, No. 2, pp. 423-429 (1981).
One of the most complex aspects of the phenomenon of planarization is the effect it has on the adjacent and surrounding topography. Mere changes in the position and size of a topographical feature can change the thickness of the film on adjacent features. The term "complex topography" for the present purposes is used to identify features that are so close to each other as to manifest interactive effects between them during the spin-coating process. The coating thickness can be increased or decreased because of this effect. It is very difficult to predict these effects before they are experimentally observed. It is also difficult to determine the polymer planarization properties from basic rheological principles.
The principle of the present invention to predict the planarization effects on the contour of a spun-coating over complex topography is based on a semi-empirical approach to first characterize the planarization properties on relatively simple topography wherein interactive effects are minimal and use such results to predict planarization phenomena on more complex topography where interactive effects are significant.
The present invention utilizes Fourier transform relationships to convert topographical features of semiconductor device patterns between the spatial domain and the frequency domain. The frequency components of the Fourier transform are weighted to provide an indication of the topographical features after they have been spun-coated as a thin film. The planarization properties of the thin film are characterized by two adjustable parameters, as will be explained in detail hereinafter. A typical spun-on thin film, in the preferred embodiment of the invention, is formed of photoresist material.